If the 4th,10th and 16th terms of a G.P. are x,y and z, respectively. Prove that x,y,z are in G.P.
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Let a be the first term and r be the common ratio of the G.P. According to the given condition, a4=ar3=x...(1)a10=ar9=y...(2)a16=ar15=z...(3)Dividing (2) by (1), we obtainxy=r3ar2⇒xy=r6Dividing (3) by (2), we obtainyz=ar9ar15⇒yz=r6∴xy=yzThus, x, y, z are in G.P.